Darren New <dne### [at] sanrrcom> wrote:
> For *every* one, there are some real numbers that do not have a finite 
> representation. That's what makes them irrational.

  "Some" is quite an understatement.

  The set of real numbers with a finite representation is countable, while
the set of real numbers without a finite representation is uncountable,
making the latter set much "larger". (The quotation marks are there because
both sets are infinite, so telling that one set is "larger" than the other
is a complicated subject, but in set theory even infinite sets can be larger
than other infinite sets, and that's the case here.)

-- 
                                                          - Warp

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